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The Virtual Element Method in Nonlinear and Fracture Solid Mechanics
The chapter presents recently developed two-dimensional Virtual Element Method (VEM) methodologies for problems of nonlinear inelastic material...
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Spectral residual method for nonlinear equations on Riemannian manifolds
In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to the problem of finding a zero of a given tangent vector field on a...
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On the quadrature exactness in hyperinterpolation
This paper investigates the role of quadrature exactness in the approximation scheme of hyperinterpolation. Constructing a hyperinterpolant of degree n ...
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The Picard-HSS-SOR iteration method for absolute value equations
In this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient...
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Geometric Constrained Scalable Algorithm for PDE-Constrained Shape Optimization
In this project, the parallel performance of shape optimization schemes is investigated using varying core counts for several levels of refinement....
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Fast Iterative Algorithms for Blind Phase Retrieval: A Survey
In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem,...
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Behavior of Newton-Type Methods Near Critical Solutions of Nonlinear Equations with Semismooth Derivatives
Having in mind singular solutions of smooth reformulations of complementarity problems, arising unavoidably when the solution in question violates...
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Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience
The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the...
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On Kosloff Tal-Ezer least-squares quadrature formulas
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of...
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The new iteration methods for solving absolute value equations
Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we...
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Fast Iterative Algorithms for Blind Phase Retrieval: A Survey
In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem,...
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Inversion of convection–diffusion equation with discrete sources
We present a convection–diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using...
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Quadratically Regularized Optimal Transport
We investigate the problem of optimal transport in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an...
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Finding the global optimum of a class of quartic minimization problem
We consider a special nonconvex quartic minimization problem over a single spherical constraint, which includes the discretized energy functional...
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Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods
We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral-element methods (DGSEMS). The use of...
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Polygons and Modular Arithmetic
There are connections between algebra and geometry that go well beyond the function–graph–analytic-geometry connections studied in high school. We...
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Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model
In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this...
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Increasing the Flexibility of the High Order Discontinuous Galerkin Framework FLEXI Towards Large Scale Industrial Applications
This paper summarizes our progress in the application and improvement of a high order discontinuous Galerkin (DG) method for scale resolving fluid...
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Nonmonotone Methods
In this chapter we introduce some globalization techniques for solving minimization problems and nonlinear equations, which relax the descent...
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Implicit Integration of Nonlinear Evolution Equations on Tensor Manifolds
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial...
